Master Your GCSE Maths: Achieve Grades 8 & 9 with 120 Challenging Problems & Step-by-Step Solutions
Are you a determined GCSE Maths student aiming for top grades? Do you crave the challenge of advanced problems that truly test your understanding and prepare you for exam success?
Look no further. This comprehensive Kindle book, "GCSE MATHS PROBLEMS", is meticulously crafted by experienced educators to help you conquer the most demanding questions and secure those elusive Grade 8 and 9 marks.
What makes this book your essential study companion?
120 Hand-Picked, Challenging Problems: Dive deep into a curated collection of advanced questions spanning Algebra, Geometry, Statistics, Number, and Ratio & Proportion. Each problem is designed to push your boundaries and deepen your conceptual understanding, mimicking the toughest questions you'll face in the actual GCSE exam.
Step-by-Step, Detailed Solutions: No more getting stuck! Every single problem comes with a clear, easy-to-follow, fully worked solution. Understand not just what the answer is, but how to get there, gaining invaluable insights into problem-solving strategies and common pitfalls.
Targeted for Grades 8 & 9: This book focuses specifically on the higher-tier content required for top grades, making it perfect for students who have mastered the basics and are ready to excel.
Aligned with All Major UK Exam Boards: Whether you're studying for AQA, Edexcel, OCR, or any other UK or Commonwealth examination board, the topics and question styles in this book are universally relevant and will strengthen your preparation.
Build Confidence & Exam Readiness: Regular practice with challenging problems is the key to success. This book provides the rigorous training needed to approach your GCSE Maths exam with confidence and a mastery mindset.
Inside, you'll find:
Algebra: Complex equations, functions, inequalities, and graphical problems.
Geometry: Advanced trigonometry, circle theorems, vectors, and 3D shapes.
Statistics & Probability: Interpreting complex data, probability trees, and advanced statistical measures.
- Number & Ratio: High-level problem-solving involving standard form, surds, and proportional reasoning.
Here are some examples:
E.g.1
Evaluate 11998² - 11988² without a calculator.
Using the difference of two squares,
11998² - 11988² = (11998 + 11988)(11998 - 11988)
= 23986 x 10
= 239860
E.g.2
Solve x - 7√x = -12
Exploring the hidden quadratic nature,
Let y = √x
y² - 7y + 12 = 0
(y - 4)(y - 3) = 0
y = 4 or y = 3
√x = 4 or √x = 3
x = 16 or x = 9
E.g.3
a) Verify Pythagoras' Theorem using the cosine rule.
b) The three sides of a triangle are 8 cm, 7 cm and 13 cm in length. Show that the largest angle of the triangle is obtuse.
a)
c² = a² + b² - 2abcosC
For a right-angled triangle, C = 90°; if hypotenuse is c,
c² = a² + b² - 2abcos90
c² = a² + b² - 2ab(0)
c² = a² + b² → Pythagoras' Theorem
b)
c² = a² + b² - 2abcosC
The largest angle of a triangle is opposite the longest side. Hence,
13² = 8² + 7² - 2x7x8xcosC
169 = 64 + 49 - 112 cos(C)
cos(C) = (113 -169)112 = -1/2
C = 120°
The largest angle is an obtuse angle.Stop guessing and start mastering! Empower yourself with the knowledge and practice to achieve your full potential in GCSE Maths. Add "Master Your GCSE Maths: Achieve Grades 8 & 9" to your Kindle library today and take the definitive step towards exam excellence.
